Origin analysis and modelling of spatially correlated noise in GNSS station coordinates

The GNSS station coordinate time series can provide fundamental data support for reference frame maintenance, geoscience research and other applications. Modelling the spatially correlated noise helps improve the accuracy of parameter estimation in GNSS coordinate time series, better serving the research in geodesy and geodynamics. This study utilizes the spatial covariance and Pearson correlation coefficients of GNSS residual series from the combined solutions of IGS third reprocessing in the UVH frame to describe the variation patterns of three-dimensional spatially correlated noise of global GNSS stations and analyze the possible sources of GNSS spatially correlated noise. The results show that the main periodic errors in the GNSS time series (such as GPS draconitic errors) are significant sources of spatially correlated noise. Furthermore, some spatially correlated noise may also originate from unmodeled geophysical signals or crustal movements. A model based on stochastic partial differential equation (SPDE) is used to fit and model the spatial correlation coefficients of white noise and power-law noise of global GNSS stations in the spherical harmonic domain. The SPDE model employed in this study effectively captures the variation in spatial correlation coefficients of white noise and power-law noise, with estimating excesses of variance at degrees 0 and 1 in the vertical direction. Besides, SPDE model significantly outperforms the exponential model in fitting the spatial correlation coefficients of global GNSS stations.